Area of a trapezoid

Geometry Level 4

In the above figure, $ADCB$ is a trapezoid. Point $E$ is the midpoint of $DC$ . If $EF=24$ and $BA=30$ , what is the area of trapezoid $ADCB$ ?

360 square units 300 square units 600 square units 720 square units

2 solutions

A Former Brilliant Member
May 26, 2017

Extend $AD$ to $G$ so that $HG$ is parallel to $AB$ and $HG$ passes through $E$ .

Since $\triangle DEG \cong \triangle HEC$ (A.S.A), $A_{AGHB}=A_{ADCB}$ .

$A_{AEB}=\dfrac{1}{2} A_{AGHB}=\dfrac{1}{2}(30)(24)=360$

$\large\therefore$ $A_{ABCD}=2(360)=720$

Ahmad Saad
May 26, 2017